A system is known from U.S. Pat. No. 5,323,575. In this known system the support member is provided with connecting elements designed in such a way that one tile assembly comprising a tile member and a tile support can be releasable connected to an adjacent tile assembly. In this way a complete tile floor can be made by interconnecting such tile assemblies. The construction, however, is such that once the floor has been completed it is extremely difficult to remove a single tile assembly without damaging the tile in a non-reparable way. This is due to the fact that the connection is made by male and female elements which are alternately used on each tile assembly. Therefore it is difficult to replace a single tile or a restricted number of tiles without a substantial damage to a number of tile assemblies.